In radio communication networks of today a user equipment communicates information over a radio link to a radio base station by performing a so called uplink (UL) transmission. In Long Term Evolution (LTE) networks an uplink channel, such as a Physical Uplink Shared Channel (PUSCH), is using a Single Carrier-Frequency Division Multiple Access (SC-FDMA) modulation scheme, which is an Orthogonal Frequency Division Multiplexing (OFDM) based modulation scheme. In such schemes the used bandwidth is divided into a multitude of orthogonal subcarriers and transmissions are, as a consequence, sensitive to the effects of frequency offset between a transmitter node, i.e. the user equipment transmitting in the UL, and a receiver node, i.e. the radio base station.
In a radio communications network a user equipment (UE) is communicating with a radio base station in the uplink (UL). There are mainly two reasons why a frequency offset occurs:
One reason is that a downlink (DL) signal transmitted by the radio base station, to which the user equipment locks its local oscillator, may be affected by a Doppler shift due to the movement of the user equipment relative to the radio base station. The user equipment moves at a velocity relative to the radio base station. The uplink signal from the user equipment to the radio base station is then again affected by the Doppler shift. Hence, the radio frequency of the uplink transmission may deviate in frequency by a frequency offset of the local oscillator and a frequency offset of the uplink transmission traveling in the air, resulting in a maximum frequency offset of
      f    offset    =            2      ×              f        d              =          2      ×                        v          ×                      f            c                          c            ⁢                          ⁢      Hz      wherefoffset is defined as the maximum frequency offset,fd is defined as the frequency offset due to Doppler effect in one transmission direction, UL or DL, which in its turn is defined as
      v    ×          f      c        cwhere v is the velocity of the user equipment and c is the speed of light and fc is a carrier frequency of the UL transmission or DL transmission.
The other reason for frequency offset is that the local oscillator in the UE may be inaccurate, which may amount to a frequency offset of up to ±0.1 parts per million (ppm) of the carrier frequency fc.
Assuming a carrier frequency, fc, of 2.5 GHz, a speed or velocity, v, of 350 km/h, and the speed of light, c, set to 3×108 m/s as in vacuum, the resulting maximum frequency offset becomes
                              f          offset                =                ⁢                              2            ×                          f              d                                +                      0.1            ×                          10                              -                6                                      ⁢                          f              c                                                              =                ⁢                                            2              ×                                                                                          350                      ×                                              10                        3                                                              3600                                    ×                  2.5                  ×                                      10                    9                                                                    3                  ×                                      10                    8                                                                        +            250                    ≈                      1870            ⁢                                                  ⁢            Hz                              
Generally in radio communications systems frequency offset estimation is based on reception of reference symbols at the receiver node. However, since the reference symbols are received twice per subframe, once per slot i.e. 0.5 ms apart, the maximum frequency offset that can be estimated is ±1000 Hz, which is a severe limitation. This can be viewed as an application of the sampling theorem. If each reference symbol is viewed as a sample, being sampled at a sampling frequency fs, where
            f      s        =                  1                  0.5          ·                      10                          -              3                                          =              2000        ⁢                                  ⁢        Hz              ,
the highest frequency in the sampled signal that can be uniquely represented is half the sampling rate, i.e. 1000 Hz, which is clearly less than what is needed for speeds around 350 km/h.
Thus, the temporal distribution of the reference symbols only allows frequency offsets up to ±1000 Hz to be estimated unambiguously and higher offsets will “wrap around” about ±1000 Hz. For example, the frequency offset +1100 Hz will be wrapped to −900 Hz leading to an erroneous estimation. This frequency offset ambiguity problem is illustrated in FIG. 1 wherein a true offset is defined along an x-axis and estimated offset along a y-axis. The estimated offset follows a curve, Cu, which is wrapped, that is, looped, when true frequency offset is going beyond ±1000 Hz as indicated by the curves Cu′, Cu″.
Another aspect of estimating frequency offset is the problem caused by mismatch between the rate of change of the offset and the rate at which receiver node can determine the offset and track the change of the offset. In high-speed train scenarios for instance, the rate of change can be very high as the train passes in close proximity to the base station, especially when the train is traveling in a tunnel.
3rd Generation Partnership Projects (3GPP) Radio Access Network (RAN) Working Group (WG) 4, known as RAN4 for short, has specified two scenarios for high-speed train conditions, one for open space and one for tunnels when using multi-antennas. Due to the Doppler shift trajectory for the tunnel scenario it is desirable to be possible to track rapid changes of the frequency offset.
After that the frequency offset has been estimated it must be compensated for in the received signal. A solution to the above identified frequency offset compensation problem would be to simply compensate time-domain samples before processing the samples by a Fast Fourier Transform (FFT) process in the receiver node. However, this method would require a compensation and an FFT per user since each user has a different frequency offset. The complexity of such a scheme thus becomes prohibitive. Existing frequency offset compensation methods exploit the fact that the reference symbols are Zadoff-Chu sequences. In, for example, the current version of the LTE standard this is only true for allocations of more than 2 resource blocks; smaller allocations use predefined sequences which are not Zadoff-Chu sequences and may not be able to use these frequency offset compensation methods.